DOI: https://doi.org/10.36719/2789-6919/56/121-128
Zulfugar Huseynov
Azerbaijan State Oil and Industry University
Master’s student
https://orcid.org/0009-0008-1303-0459
zulfuqarrhuseynovv@gmail.com
Exponential Accumulation Method for Solving Boundary Integral
Equations Over Polygons
Abstract
The boundary integral equation of potential theory is considered for the interior Dirichlet problem for the Laplace operator and a system of boundary integral equations for the first boundary value problem of plane elasticity theory in domains with a finite number of corner points. Estimates are given for the derivatives of the kernels and solutions of these types of integral equations on curves that are the boundaries of simply connected polygons, and a numerical solution method is constructed based on the use of the same family of composite quadrature formulas. The exponential rate of convergence of the method with respect to the number of nodes of the quadrature formula used is proven.
Keywords: integral, equation, polygons, exponential accumulation method